Problem: Simplify the following expression: $k = \dfrac{20x - 50y}{40z - 10y} + \dfrac{30z - 30y}{40z - 10y}$ You can assume $x,y,z \neq 0$.
Explanation: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{20x - 50y + 30z - 30y}{40z - 10y}$ $k = \dfrac{20x - 80y + 30z}{40z - 10y}$ The numerator and denominator have a common factor of $10$, so we can simplify $k = \dfrac{2x - 8y + 3z}{4z - y}$